Inverting such an argument suggests that possibly the simplest way to generate random multifractal weights in the lattice
is by constructing quantities \(\ln {p_i}\)  at every lattice site \(i\)  as Gaussian-distributed random variables correlated
in precisely the way prescribed by (REF ).
The resulting model has a very natural interpretation in terms of the equilibrium
statistical mechanics. Indeed, consider a single classical particle subject to a random Gaussian
potential \(V({\bf x})\) . It is the standard fact of theory of random processes[1]}
that if such a particle moves under the influence of
the thermal white noise according to the Langevin equation
\(\dot{\bf x}=-\frac{\partial }{\partial {\bf x}}V\left({\bf x}\right)+\xi ({\bf x},t), \quad \overline{\xi ({\bf x_1},t_1)\xi ({\bf x_2},t_2)}=2T\delta (t_1-t_2)\) 
